The works of Hassett and Kuznetsov identify countably many divisors $C_d$ inthe open subset of$mathbbP^55=mathbbP(H^0(mathcalO_mathbbP^5(3)))$ parametrizingall cubic 4-folds and conjecture that the cubics corresponding to thesedivisors are precisely the rational ones. Rationality has been knownclassically for the first family $C_14$. We use congruences of 5-secantconics to prove rationality for the first three of the families $C_d$,corresponding to $d=14, 26, 38$ in Hassett's notation.

Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds

Francesco Russo
;
Giovanni Staglianò
2019

Abstract

The works of Hassett and Kuznetsov identify countably many divisors $C_d$ inthe open subset of$mathbbP^55=mathbbP(H^0(mathcalO_mathbbP^5(3)))$ parametrizingall cubic 4-folds and conjecture that the cubics corresponding to thesedivisors are precisely the rational ones. Rationality has been knownclassically for the first family $C_14$. We use congruences of 5-secantconics to prove rationality for the first three of the families $C_d$,corresponding to $d=14, 26, 38$ in Hassett's notation.
Mathematics - Algebraic Geometry; Mathematics - Algebraic Geometry; 14E08, 14J25, 14N05
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/358646
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